The Sun says he told Wilshere he is playing for his Arsenal future in a tense phone call before he left on loan.
The Arsenal boss reluctantly let Wilshere join Bournemouth after heart-to-heart talks on Monday.
But he was left in no doubt his move must work out if he is to revive his career at the Emirates.
The England midfielder asked to go on loan after he was left out of Sam Allardyce's first England squad last Sunday.
Wenger told him to see the chance to become a more rounded footballer and use the experience at Bournemouth wisely.